Question

If $X$ and $Y$ are independent binomial variate $B(5,1/2)$ and $B(7,1/2)$, then $P(X+Y=3)$ is

• A. $55/1024$
• B. $55/4098$
• C. $55/2048$
• D. None of these

Answer 1

The correct option is A $55/1024$

Using $X+Y\sim B(12,1/2)$
Required probability $P(X+Y=3){=}^{12}{C}_3{\left(\frac{1}{2}\right)}^{12}=\frac{55}{1024}$